Abstract The fascination for lanthanide optical spectroscopy dates back to the .....
Note that if the sub-shell is half filled, then L = 0 and J = S. Additionally, J may.
Basics of Lanthanide Photophysics Jean-Claude G. Bu¨nzli and Svetlana V. Eliseeva
Abstract The fascination for lanthanide optical spectroscopy dates back to the 1880s when renowned scientists such as Sir William Crookes, LeCoq de Boisbaudran, Euge`ne Demarc¸ay or, later, Georges Urbain were using luminescence as an analytical tool to test the purity of their crystallizations and to identify potential new elements. The richness and complexity of lanthanide optical spectra are reflected in an article published in 1937 by J.H. van Vleck: The Puzzle of Rare Earth Spectra in Solids. After this analytical and exploratory period, lanthanide unique optical properties were taken advantage of in optical glasses, filters, and lasers. In the mid-1970s, E. Soini and I. Hemmila¨ proposed lanthanide luminescent probes for time-resolved immunoassays (Soini and Hemmila¨ in Clin Chem 25:353–361, 1979) and this has been the starting point of the present numerous bio-applications based on optical properties of lanthanides. In this chapter, we first briefly outline the principles underlying the simplest models used for describing the electronic structure and spectroscopic properties of trivalent lanthanide ions LnIII (4fn) with special emphasis on luminescence. Since the book is intended for a broad readership within the sciences, we start from scratch defining all quantities used, but we stay at a descriptive level, leaving out detailed mathematical developments. For the latter, the reader is referred to references Liu and Jacquier, Spectroscopic properties of rare earths in optical materials. Tsinghua University Press & Springer, Beijing & Heidelberg, 2005 and Go¨rller-Walrand and Binnemans, Rationalization of crystal field parameters. In: Gschneidner, Eyring (eds) Handbook on the physics and chemistry of rare earths, vol 23. Elsevier BV, Amsterdam, Ch 155, 1996. The second part of the chapter is devoted to practical aspects of lanthanide luminescent probes, both from the point of view of their design and of their potential utility.
J.-C.G. Bu¨nzli (*) and S.V. Eliseeva Laboratory of Lanthanide Supramolecular Chemistry, E´cole Polytechnique Fe´de´rale de Lausanne, BCH 1402, 1015 Lausanne, Switzerland e-mail:
[email protected]
P. Ha¨nninen and H. Ha¨rma¨ (eds.), Lanthanide Luminescence: Photophysical, Analytical and Biological Aspects, Springer Ser Fluoresc (2010), DOI 10.1007/4243_2010_3, # Springer-Verlag Berlin Heidelberg 2010
J.-C.G. Bu¨nzli and S.V. Eliseeva
Keywords Crystal-field analysis Energy transfer f–f Transition Intrinsic quantum yield Lanthanide bioprobe Lanthanide luminescence Lanthanide spectroscopy Lifetime Luminescence sensitization Population analysis Quantum yield Radiative lifetime Selection rule Site symmetry Stern–Volmer quenching
Contents 1
Electronic Structure of Trivalent Lanthanide Ions 1.1 Atomic Orbitals 1.2 Electronic Configuration 1.3 The Ions in a Ligand Field 2 Absorption Spectra 2.1 Induced ED f–f Transitions: Judd–Ofelt Theory [5, 6] 2.2 4f–5d and CT Transitions 3 Emission Spectra 4 Sensitization of Lanthanide Luminescence 4.1 Design of Efficient Lanthanide Luminescent Bioprobes 4.2 Practical Measurements of Absolute Quantum Yields 5 Information Extracted from Lanthanide Luminescent Probes 5.1 Metal Ion Sites: Number, Composition, and Population Analysis 5.2 Site Symmetry Through Crystal-Field Analysis 5.3 Strength of Metal–Ligand Bonds: Vibronic Satellite Analysis 5.4 Solvation State of the Metal Ion 5.5 Energy Transfers: Donor–Acceptor Distances and Control of the Photophysical Properties of the Acceptor by the Donor 5.6 FRET Analysis 5.7 Ligand Exchange Kinetics 5.8 Analytical Probes 6 Appendices 6.1 Site Symmetry Determination from EuIII Luminescence Spectra 6.2 Examples of Judd–Ofelt Parameters 6.3 Examples of Reduced Matrix Elements 6.4 Emission Spectra References
Abbreviations AO CF CT DMF DNA dpa dtpa EB ED
Acridine orange Crystal field Charge transfer Dimethylformamide Deoxyribonucleic acid Dipicolinate (2,6-pyridine dicarboxylate) Diethylenetrinitrilopentaacetate Ethidium bromide Electric dipole
Basics of Lanthanide Photophysics
EQ FRET hfa ILCT ISC JO LLB LMCT MD MLCT NIR PCR SO tta YAG
Electric quadrupole Fo¨rster resonant energy transfer Hexafluoroacetylacetonate Intraligand charge transfer Intersystem crossing Judd–Ofelt Lanthanide luminescent bioprobe Ligand-to-metal charge transfer Magnetic dipole Metal-to-ligand charge transfer Near-infrared Polymerase chain reaction Spin–orbit Thenoyltrifluoroacetylacetonate Yttrium aluminum garnet
1 Electronic Structure of Trivalent Lanthanide Ions 1.1
Atomic Orbitals
In quantum mechanics, three variables depict the movement of the electrons around the positively-charged nucleus, these electrons being considered as waves with wavelength l ¼ h/mv where h is Planck’s constant (6.626 1034 J s1), m and v the mass (9.109 1031 kg) and velocity of the electron, respectively: – The time-dependent Hamiltonian operator H describing the sum of kinetic and potential energies in the system; it is a function of the coordinates of the electrons and nucleus. – The wavefunction, Cn, also depending on the coordinates and time, related to the movement of the particles, and not directly observable; its square (Cn)2 though gives the probability that the particle it describes will be found at the position given by the coordinates; the set of all probabilities for a given electronic Cn, is called an orbital. – The quantified energy En associated with a specific wavefunction, and independent of the coordinates. These quantities are related by the dramatically simple Schro¨dinger equation, which replaces the fundamental equations of classical mechanics for atomic systems: HCn ¼ En Cn :
(1)
Energies En are eigenvalues of Cn, themselves called eigenfunctions. In view of the complexity brought by the multidimensional aspect of this equation
J.-C.G. Bu¨nzli and S.V. Eliseeva
(3 coordinates for each electron and nucleus, in addition to time) several simplifications are made. Firstly, the energy is assumed to be constant with time, which removes one coordinate. Secondly, nuclei being much heavier than electrons, they are considered as being fixed (Born–Oppenheimer approximation). Thirdly, since the equation can only be solved precisely for the hydrogen atom, the resulting hydrogenoid or one-electron wavefunction is used for the other elements, with a scaling taking into account the apparent nucleus charge, i.e., including screening effects from the other electrons. Finally, to ease solving the equation for non-H atoms, the various interactions occurring in the electron-nucleus system are treated separately, in order of decreasing importance (perturbation method). For hydrogen, the Hamiltonian simply reflects Coulomb’s attraction between the nucleus and the electron, separated by a distance ri, and the kinetic energy of the latter:1 1 1 H0 ¼ Di ri 2
@2 @2 @2 D¼ þ þ : @x2 @y2 @z2
(2)
Each wavefunction (or orbital: the two terms are very often, but wrongly, taken as synonyms) resulting from solving (1) is defined by four quantum numbers reflecting the quantified energy of the two motions of the electrons: the orbital motion, defined by the angular momentum ~ ‘, and the spin, characterized by the angular momentum ~ s. If polar coordinates (r, #, ’) are used, wavefunctions are expressed as the product of a normalizing factor N, of a radial function ð2‘ þ 1Þ; J ¼ Jmax :
Note that if the sub-shell is half filled, then L = 0 and J = S. Additionally, J may take half-integer values if S is half-integer. The set of levels is referred to as a multiplet and this multiplet is a regular one if n < (2ℓ + 1), the energy of the levels increasing with increasing values of J, while it is inverted if n > (2ℓ + 1). This is illustrated with EuIII (4f6) for which the ground level is 7F0 while it is 7F6 for TbIII (4f8). Finally, the energy difference between two consecutive spin–orbit levels with quantum numbers J and J0 = J + 1 is directly proportional to J0 : DE ¼ l J 0 :
(8)
The electronic properties of the trivalent 4f free ions are summarized in Table 1.
1.3
The Ions in a Ligand Field
The above developments are valid for free ions. When a LnIII ion is inserted into a chemical environment, the spherical symmetry of its electronic structure is destroyed and the remaining (2J þ 1) degeneracy of its spectroscopic levels is partly lifted, depending on the exact symmetry of the metal–ion site. In view of the
J.-C.G. Bu¨nzli and S.V. Eliseeva Table 1 Electronic properties of LnIII free ions fn Multiplicity No. of terms No. of levels Ground level z/cm1,a l/cm1,a 0 14 1 1 f f 1 1 1 S0 S0 – – – – 2 1 2 F5/2 2F7/2 625 2,870 625 2,870 f1 f13 14 3 7 13 H4 3H6 740 2,628 370 1,314 f2 f12 91 4 17 41 I9/2 4I15/2 884 2,380 295 793 f3 f11 364 5 5 47 107 I4 I8 1,000 2,141 250 535 f4 f10 1,001 6 73 198 H5/2 6H15/2 1,157 1,932 231 386 f5 f9 2,002 7 6 8 7 3,003 119 295 F0 F6 1,326 1,709 221 285 f f 8 3,432 119 327 S7/2 1,450 0 f7 a For aqua ions, except for CeIII (Ce:LaCl3) and YbIII (Yb3Ga5O12), from [2]. The first column refers to f1–7 and the second to f8–14
inner character of the 4f wavefunctions their mixing with the surrounding orbitals remains small and so is the resulting level splitting (a few hundreds of cm1), so that this perturbation can be treated last. Nevertheless, the resulting Hamiltonian gets very complex, so that a simplifying concept has been put forward by H. Bethe in 1929: the ligands are replaced by (negative) point charges generating a crystal (or ligand) electrostatic field which, in turn, interacts with the moving 4f electrons, generating a ligand-field (or crystal-field, or Stark) splitting of the spectroscopic levels. With the parameterization introduced by B. G. Wybourne in 1965, the final Hamiltonian becomes: H¼
X n n X X Z0 1 1 ~ S~ þ Di þ þlL Bkq CðkÞ q ðiÞ; 2 r r i i¼1 k;q;i i6¼j ij
(9)
where the summation involving i is on all the 4f electrons, Bqk are ligand-field parameters, commonly treated as phenomenological parameters, and C(k)q are components of tensor operators C(k) which transform like the spherical harmonics used for the analytical form of the 4f wavefunctions. The running number k must be even and smaller than 2ℓ; for 4f electrons it can, therefore, take values of 0, 2, 4, and 6. The values for q are restricted by the point group of symmetry into which the LnIII ion is embedded, but in any case, jqj k. The Bqk parameters may be complex numbers but they have to be real for any symmetry group with a 180 rotation about the y axis or with the xy plane being a mirror plane. The relationship between the 32 crystallographic symmetry groups and the Bqk parameters is given in Table 2. In order to compare the ligand field strengths in different compounds, F. Auzel has proposed the following expression for an “average” total ligand-field effect: "
2 #1=2 1 X ðBkq Þ Nv ¼ : 4p k;q ð2k þ 1Þ
(10)
Basics of Lanthanide Photophysics Table 2 Non-zero crystal-field parameters for fn electronic configurations and examples of corresponding crystal hosts [1] Symmetry Site symmetry Crystal field parameters Example 2 4 6 2 4 6 4 6 6 LaF3 Monoclinic C1, CS, C2, C2h, B0 ; B0 ; B0 ;
